This invention relates to tomographic imaging, and more particularly to methods and apparatus for reducing aliasing artifacts in computerized tomographic (CT) imaging in a twin beam imaging system.
In at least one known CT imaging system configuration, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system and generally referred to as an xe2x80x9cimaging planexe2x80x9d. The x-ray beam passes through an object being imaged, such as a patient. The beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is dependent upon the attenuation of an x-ray beam by the object. Each detector element of the array produces a separate electrical signal that is a measurement of the beam attenuation at the detector location. The attenuation measurements from all the detectors are acquired separately to produce a transmission profile.
In known third generation CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around the object to be imaged so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry angle is referred to as a xe2x80x9cviewxe2x80x9d. A xe2x80x9cscanxe2x80x9d of the object comprises a set of views made at different gantry angles, or view angles, during one revolution of the x-ray source and detector.
In an axial scan, the projection data is processed to construct an image that corresponds to a two dimensional slice taken through the object. One method for reconstructing an image from a set of projection data is referred to in the art as the filtered back projection technique. This process converts the attenuation measurements from a scan into integers called xe2x80x9cCT numbersxe2x80x9d or xe2x80x9cHounsfield unitsxe2x80x9d, which are used to control the brightness of a corresponding pixel on a cathode ray tube display.
To reduce the total scan time, a xe2x80x9chelicalxe2x80x9d scan may be performed. To perform a xe2x80x9chelicalxe2x80x9d scan, the patient is moved while the data for the prescribed number of slices is acquired. Such a system generates a single helix from a one fan beam helical scan. The helix mapped out by the fan beam yields projection data from which images in each prescribed slice may be reconstructed.
Reconstruction algorithms for helical scanning typically use helical weighing algorithms which weight the collected data as a function of view angle and detector channel index. Specifically, prior to filtered back projection, the data is weighted according to a helical weighing factor, which is a function of both the gantry angle and detector angle. The helical weighting algorithms also scale the data according to a scaling factor, which is a function of the distance between the x-ray source and the object. The weighted and scaled data is then processed to generate CT numbers and to construct an image that corresponds to a two dimensional slice taken through the object.
In some known clinical scans, projection weighting prior to image reconstruction is performed. For example, halfscan weighting has been implemented to shorten scan time by approximately 40%. Underscan weighting is used to suppress patient motion in axial scan protocols. On the other hand, helical weightings (xe2x80x9cHigh Qualityxe2x80x9d or HQ mode, and xe2x80x9cHigh Speedxe2x80x9d or HS mode, for example) have been used to avoid artifacts resulting from constant table translation during a scan. However, because of a lack of quarter-detector offset, halfscan sampling without focal spot deflection typically does not produce aliasing-free images for high-resolution kernels.
In one aspect, a method for weighting projection data is provided. The method includes helically twin beam scanning an object at a selected pitch to acquire a first data sample from a first detector row and a second data sample from a second detector row. The first data sample includes first conjugate data and first two pi data. The second data sample includes second conjugate data and second two pi data. The first conjugate data and the second conjugate data are conjugate each other, and the first two pi data and the second two pi data are two xcfx80 projection angle apart. The method also includes identifying a center view of the first conjugate data and the second conjugate data, and weighting at least one of the first conjugate data, the second conjugate data, the first two pi data, and the second two pi data inverse to the identified center view.
In another aspect, a method for weighting projection data is provided. The method includes helically twin beam scanning an object at a selected pitch to acquire a first data sample from a first detector row and a second data sample from a second detector row. The first data sample includes first conjugate data and first two pi data. The second data sample includes second conjugate data and second two pi data. The first conjugate data and the second conjugate data are conjugate each other, and the first two pi data and the second two pi data are two xcfx80 projection angle apart. The method also includes identifying a center view of the first conjugate data and the second conjugate data, wherein the center view is xcfx80/p from xcex21 and xcfx80/p from xcex22. Wherein p is a helical pitch, xcex21 is the projection angle at which the first detector row intersects a plane of reconstruction, and xcex22 is the projection angle at which the second detector row intersects the plane of reconstruction. The method also includes weighting the first data sample according to             w      1        ⁡          (              γ        ,        β            )        =      {                                                      (                                                β                  -                  β2                  +                                      2                    ⁢                    π                                                                    β1                  -                  β2                  +                                      2                    ⁢                    π                                                              )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        +                                                  2                          ⁢                          π                                                -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β2              -                              2                ⁢                π                                      ≤            β            ≤                          β0              -              π                                                                                      (                                                β                  -                  β2                  +                                      2                    ⁢                    π                                                                    β1                  -                  β2                  +                                      2                    ⁢                    π                                                              )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                                            )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -              π                        ≤            β            ≤            β1                                                                          (                                                β2                  -                  β                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                                            )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                            β1            ≤            β             less than                           β0              -                              2                ⁢                γ                                                                                                    (                                                β2                  -                  β                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -                              2                ⁢                γ                                      ≤            β             less than             β2                              
and weighting the second data sample according to             w      2        ⁡          (              γ        ,        β            )        =      {                                                      (                                                β                  -                  β1                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                    (                                          1                      -                                              2                        ⁢                        α                                                              )                                    ⁢                                      (                                          β0                      -                                              2                        ⁢                        γ                                            -                      β                                        )                                                                    π                  -                                      2                    ⁢                    γ                                                              ]                                                            β1            ≤            β            ≤                          β0              -                              2                ⁢                γ                                                                                                    (                                                β                  -                  β1                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -                              2                ⁢                γ                                      ≤            β             less than             β2                                                                          (                                                β1                  +                                      2                    ⁢                    π                                    -                  β                                                  β1                  +                  π                  -                  β2                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                            β2            ≤            β             less than                           β0              +              π                                                                                      (                                                β1                  +                                      2                    ⁢                    π                                    -                  β                                                  β1                  +                  π                  -                  β2                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                        +                                                  2                          ⁢                          π                                                                    )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              +              π                        ≤            β             less than                           β1              +                              2                ⁢                π                                                        
where xcex2 is a projection angle, xcex20 is the identified center view, xcex3 is a fan angle, and xcex1 is a relative strength parameter.
In a further aspect, a twin beam computerized tomographic (CT) imaging system for imaging an object is provided. The imaging system includes a detector array, at least one radiation source, and a computer coupled to the detector array and radiation source. The computer is configured to helically twin beam scan an object at a selected pitch to acquire a first data sample from a first detector row and a second data sample from a second detector row. The first data sample including first conjugate data and first two pi data. The second data sample including second conjugate data and second two pi data. The first conjugate data and the second conjugate data are conjugate each other, and the first two pi data and the second two pi data are two xcfx80 projection angle apart. The computer is also configured to identify a center view of the first conjugate data and the second conjugate data, and weight at least one of the first conjugate data, the second conjugate data, the first two pi data, and the second two pi data inverse to the identified center view. The computer is also configured to filter and backproject the weighted projection data to generate an image of the object.
In one aspect, a twin beam computerized tomographic (CT) imaging system for imaging an object is provided. The imaging system includes a detector array, at least one radiation source, and a computer coupled to the detector array and radiation source. The computer is configured to helically twin beam scan an object at a selected pitch to acquire a first data sample from a first detector row and a second data sample from a second detector row. The first data sample includes first conjugate data and first two pi data. The second data sample includes second conjugate data and second two pi data. The first conjugate data and the second conjugate data are conjugate each other, and the first two pi data and the second two pi data are two xcfx80 projection angle apart. The computer is also configured to identify a center view of the first conjugate data and the second conjugate data, weight the first data sample according to             w      1        ⁡          (              γ        ,        β            )        =      {                                                      (                                                β                  -                  β2                  +                                      2                    ⁢                    π                                                                    β1                  -                  β2                  +                                      2                    ⁢                    π                                                              )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        +                                                  2                          ⁢                          π                                                -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β2              -                              2                ⁢                π                                      ≤            β            ≤                          β0              -              π                                                                                      (                                                β                  -                  β2                  +                                      2                    ⁢                    π                                                                    β1                  -                  β2                  +                                      2                    ⁢                    π                                                              )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                                            )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -              π                        ≤            β            ≤            β1                                                                          (                                                β2                  -                  β                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                                            )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                            β1            ≤            β             less than                           β0              -                              2                ⁢                γ                                                                                                    (                                                β2                  -                  β                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -                              2                ⁢                γ                                      ≤            β             less than             β2                              
and weight the second data sample according to             w      2        ⁡          (              γ        ,        β            )        =      {                                                      (                                                β                  -                  β1                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                    (                                          1                      -                                              2                        ⁢                        α                                                              )                                    ⁢                                      (                                          β0                      -                                              2                        ⁢                        γ                                            -                      β                                        )                                                                    π                  -                                      2                    ⁢                    γ                                                              ]                                                            β1            ≤            β            ≤                          β0              -                              2                ⁢                γ                                                                                                    (                                                β                  -                  β1                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -                              2                ⁢                γ                                      ≤            β             less than             β2                                                                          (                                                β1                  +                                      2                    ⁢                    π                                    -                  β                                                  β1                  +                  π                  -                  β2                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                            β2            ≤            β             less than                           β0              +              π                                                                                      (                                                β1                  +                                      2                    ⁢                    π                                    -                  β                                                  β1                  +                  π                  -                  β2                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                        +                                                  2                          ⁢                          π                                                                    )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              +              π                        ≤            β             less than                           β1              +                              2                ⁢                π                                                        
where xcex2 is a projection angle, xcex20 is the identified center view, xcex21 is the projection angle at which the first detector row intersects a plane of reconstruction, xcex22 is the projection angle at which the second detector row intersects the plane of reconstruction, xcex3 is a fan angle, and xcex1 is a relative strength parameter.
In another aspect, a computer readable medium encoded with a program executable by a computer for reconstructing a three-dimensional dataset representative of an imaged object is provided. The program is configured to instruct the computer to helically twin beam scan an object at a selected pitch to acquire a first data sample from a first detector row and a second data sample from a second detector row. The first data sample including first conjugate data and first two pi data. The second data sample including second conjugate data and second two pi data. The first conjugate data and the second conjugate data are conjugate each other, and the first two pi data and the second two pi data are two xcfx80 projection angle apart. The program is also configured to instruct the computer to identify a center view of the first conjugate data and the second conjugate data, and weight at least one of the first conjugate data, the second conjugate data, the first two pi data, and the second two pi data inverse to the identified center view. The program is also configured to instruct the computer to filter and backproject the weighted projection data to generate an image of the object.
In a further aspect, a computer readable medium encoded with a program executable by a computer for reconstructing a three-dimensional dataset representative of an imaged object is provided. The program is configured to instruct the computer to helically twin beam scan an object at a selected pitch to acquire a first data sample from a first detector row and a second data sample from a second detector row. The first data sample includes first conjugate data and first two pi data. The second data sample includes second conjugate data and second two pi data. The first conjugate data and the second conjugate data are conjugate each other, and the first two pi data and the second two pi data are two xcfx80 projection angle apart. The program is also configured to instruct the computer to identify a center view of the first conjugate data and the second conjugate data; wherein the center view is xcfx80/p from a first projection region and xcfx80/p from a third projection region, wherein p is a helical pitch. The program is also configured to instruct the computer to weight the first data sample according to             w      1        ⁡          (              γ        ,        β            )        =      {                                                      (                                                β                  -                  β2                  +                                      2                    ⁢                    π                                                                    β1                  -                  β2                  +                                      2                    ⁢                    π                                                              )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        +                                                  2                          ⁢                          π                                                -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β2              -                              2                ⁢                π                                      ≤            β            ≤                          β0              -              π                                                                                      (                                                β                  -                  β2                  +                                      2                    ⁢                    π                                                                    β1                  -                  β2                  +                                      2                    ⁢                    π                                                              )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                                            )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -              π                        ≤            β            ≤            β1                                                                          (                                                β2                  -                  β                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                                            )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                            β1            ≤            β             less than                           β0              -                              2                ⁢                γ                                                                                                    (                                                β2                  -                  β                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -                              2                ⁢                γ                                      ≤            β             less than             β2                              
and weight the second data sample according to             w      2        ⁡          (              γ        ,        β            )        =      {                                                      (                                                β                  -                  β1                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                    (                                          1                      -                                              2                        ⁢                        α                                                              )                                    ⁢                                      (                                          β0                      -                                              2                        ⁢                        γ                                            -                      β                                        )                                                                    π                  -                                      2                    ⁢                    γ                                                              ]                                                            β1            ≤            β            ≤                          β0              -                              2                ⁢                γ                                                                                                    (                                                β                  -                  β1                                                  β2                  -                  β1                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              -                              2                ⁢                γ                                      ≤            β             less than             β2                                                                          (                                                β1                  +                                      2                    ⁢                    π                                    -                  β                                                  β1                  +                  π                  -                  β2                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β                        -                        β0                        +                                                  2                          ⁢                          γ                                                                    )                                                                            π                    +                                          2                      ⁢                      γ                                                                      +                α                            ]                                                            β2            ≤            β             less than                           β0              +              π                                                                                      (                                                β1                  +                                      2                    ⁢                    π                                    -                  β                                                  β1                  +                  π                  -                  β2                                            )                        ⁡                          [                                                                                          (                                              1                        -                                                  2                          ⁢                          α                                                                    )                                        ⁢                                          (                                              β0                        -                                                  2                          ⁢                          γ                                                -                        β                        +                                                  2                          ⁢                          π                                                                    )                                                                            π                    -                                          2                      ⁢                      γ                                                                      +                α                            ]                                                                          β0              +              π                        ≤            β             less than                           β1              +                              2                ⁢                π                                                        
where ,xcex2 is a projection angle, xcex20 is the identified center view, ⊕1 is the projection angle at which the first detector row intersects a plane of reconstruction, xcex22 is the projection angle at which the second detector row intersects the plane of reconstruction, xcex3 is a fan angle, and xcex1 is a relative strength parameter.